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Chapter 14: Problem 89

Calculate the \(\mathrm{pH}\) of the following solutions. a. \(0.10 \mathrm{M} \mathrm{NaOH}\) b. \(1.0 \times 10^{-10} M \mathrm{NaOH}\) c. \(2.0 \mathrm{M} \mathrm{NaOH}\)

Short Answer

Expert verified
The pH values of the given solutions are: a. \(\mathrm{pH} \approx 13\) for \(0.10 \mathrm{M}\ \mathrm{NaOH}\) b. \(\mathrm{pH} \approx 4\) for \(1.0 \times 10^{-10} M\ \mathrm{NaOH}\) c. \(\mathrm{pH} \approx 14.3\) for \(2.0 \mathrm{M}\ \mathrm{NaOH}\)

Step by step solution

01

1. Determining the \(\mathrm{OH}^-\) concentration in each solution

Since the given concentrations are for \(\mathrm{NaOH}\) and this is a strong base that dissociates completely in water, we can assume that the concentration of \(\mathrm{OH}^-\) ions is equal to the concentration of \(\mathrm{NaOH}\) in each solution: a. For \(0.10 \mathrm{M} \mathrm{NaOH}\), \([\mathrm{OH}^-] = 0.10 \mathrm{M}\) b. For \(1.0 \times 10^{-10} M \mathrm{NaOH}\), \([\mathrm{OH}^-] = 1.0 \times 10^{-10} M\) c. For \(2.0 \mathrm{M} \mathrm{NaOH}\), \([\mathrm{OH}^-] = 2.0 \mathrm{M}\)
02

2. Calculating the \(\mathrm{pOH}\) of each solution

Now that we have the concentration of \(\mathrm{OH}^-\) ions in each solution, we can calculate their respective \(\mathrm{pOH}\) values using the formula \(\mathrm{pOH} = -\log{[\mathrm{OH}^-]}\): a. \(\mathrm{pOH}_a = -\log{(0.10)}\) b. \(\mathrm{pOH}_b = -\log{(1.0 \times 10^{-10})}\) c. \(\mathrm{pOH}_c = -\log{(2.0)}\) Calculating these values, we get: a. \(\mathrm{pOH}_a \approx 1\) b. \(\mathrm{pOH}_b \approx 10\) c. \(\mathrm{pOH}_c \approx -0.3\)
03

3. Calculating the \(\mathrm{pH}\) of each solution

Finally, we can find the \(\mathrm{pH}\) of each solution using the relationship between \(\mathrm{pH}\) and \(\mathrm{pOH}\) (\(\mathrm{pH} + \mathrm{pOH} = 14\)): a. \(\mathrm{pH}_a = 14 - \mathrm{pOH}_a = 14 - 1 = 13\) b. \(\mathrm{pH}_b = 14 - \mathrm{pOH}_b = 14 - 10 = 4\) c. \(\mathrm{pH}_c = 14 - \mathrm{pOH}_c = 14 - (-0.3) \approx 14.3\) Therefore, the \(\mathrm{pH}\) values of the given solutions are: a. \(\mathrm{pH} \approx 13\) for \(0.10 \mathrm{M}\ \mathrm{NaOH}\) b. \(\mathrm{pH} \approx 4\) for \(1.0 \times 10^{-10} M\ \mathrm{NaOH}\) c. \(\mathrm{pH} \approx 14.3\) for \(2.0 \mathrm{M}\ \mathrm{NaOH}\)

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Write the reaction and the corresponding \(K_{\mathrm{b}}\) equilibrium expression for each of the following substances acting as bases in water. a. aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) b. dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\)

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